Abstract
In this work, we study two-dimensional Galilean field theories with global translations and anisotropic scaling symmetries. We show that such theories have enhanced local symmetries, generated by the infinite dimensional spin-l Galilean algebra with possible central extensions, under the assumption that the dilation operator is diagonalizable and has a discrete and non-negative spectrum. We study the Newton-Cartan geometry with anisotropic scaling, on which the field theories could be defined in a covariant way. With the well-defined Newton-Cartan geometry we establish the state-operator correspondence in anisotropic GCFT, determine the two-point functions of primary operators, and discuss the modular properties of the torus partition function which allows us to derive Cardy-like formulae.
Highlights
In two-dimensional(2D) spacetime, the global symmetry in a quantum field theory could be enhanced to a local one
For the Galilean CFT with anisotropic scaling discussed in this paper, we show that it should be defined on a Newton-Cartan geometry with additional scaling structure, similar to the warped geometry discussed in [4]
In the present work we studied a class of general Galilean conformal field theories (GCFT) with anisotropic scaling x → λcx, y → λdy
Summary
In two-dimensional(2D) spacetime, the global symmetry in a quantum field theory could be enhanced to a local one. The study of consistent asymptotical boundary conditions and corresponding asymptotic symmetry group have played important roles in setting up other holographic correspondences beyond AdS=CFT, including chiral gravity [40], WAdS/WCFT [41,42], Kerr/CFT [43], Bondi-Metzner-Sachs (BMS)/Galilean conformal algebra (GCA)[16,17], BMS/CFT [44,45,46] and the nonrelativistic limit of the AdS=CFT [18] Recall that both WCFT and GCA are the special cases in our study; it is tempting to guess that the anisotropic GCFT could be the holographic dual of a gravity theory. The geometries related by local scaling and Galilean boost belong to the same equivalent class.4 Having defined these theories, we find the infinitely many conserved charges by considering the currents coupled to the geometric quantities.
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